StartUpDG

Routines to initialize reference element operators, physical mesh arrays, and connectivity for nodal discontinuous Galerkin (DG) methods. Codes roughly based on Nodal Discontinuous Galerkin Methods by Hesthaven and Warburton (2007). The original port from Matlab to Julia was by Yimin Lin, with subsequent modifications by Jesse Chan.

This package is registered and can be installed via ] add StartUpDG.

Usage overview

Variables are contained within structs rd::RefElemData and md::MeshData, which contain quantities from Globals1D, Globals2D, Globals3D in the Nodal DG book codes. These can be used to compute DG derivatives, and are useful for matrix-free implementations of DG methods using explicit time-stepping.

using StartUpDG

# polynomial degree and mesh size
N = 3
K1D = 8

# init ref element and mesh
rd = RefElemData(Tri(), N)
VXY, EToV = uniform_mesh(Tri(), K1D)
md = MeshData(VXY, EToV, rd)

# Define a function by interpolation
(; x, y) = md
u = @. 2 + .5*exp(-100*(x^2 + y^2))

# Compute derivatives using geometric mapping + chain rule
(; Dr, Ds) = rd
(; rxJ, sxJ, J) = md
dudx = (rxJ .* (Dr*u) + sxJ .* (Ds*u)) ./ J

Contributors

• SBP nodal points were contributed by Ethan Kubatko and Jason Hicken.
• Hendrik Ranocha contributed to array types used in cut-cell and hybrid meshes.
• Mason McCallum contributed Gmsh reading capabilities
• David Knapp contributed VTK visualization capabilities and tensor product wedges.